Question

Find dy/dx by implicit differentiation. x2 − 8xy + y2 = 8

Answer 1

We have that

x² − 8xy + y² = 8
2x-8y-8x(dy/dx)+2y*(dy/dx)=0
8x(dy/dx)-2y*(dy/dx)=2x-8y
[8x-2y]*(dy/dx)=2x-8y
(dy/dx)=[2x-8y]/[8x-2y]
(dy/dx)=2*[x-4y]/2*[4x-y]
(dy/dx)=[x-4y]/[4x-y]

the answer is
(dy/dx)=[x-4y]/[4x-y]

Answer 2

Answer:

$\frac{dy}{dx} = \frac{8y - 2x}{2y - 8x}$

Step-by-step explanation:

The denominator is always the variable that we want to find the derivation in relation of. So it is always dx.

The number is the variable we derivated. So

$x^{2} - 8xy + y^{2} = 8$

$2x\frac{dx}{dx} - 8y\frac{dx}{dx} - 8x\frac{dy}{dx} + 2y\frac{dy}{dx} = 0$

$2x - 8y + (2y - 8x)\frac{dy}{dx} = 0$

$(2y - 8x)\frac{dy}{dx} = 8y - 2x$

$\frac{dy}{dx} = \frac{8y - 2x}{2y - 8x}$